Anomalous diffusion for a correlated process with long jumps

Details Anomalous diffusion for a correlated process with long jumps Anomalous diffusion for a correlated process with long jumps

2011-06-20

arxiv.org/abs/1106.3893v1

Physica A 390 (2011) 3077--3085

Physics

Condensed Matter

Statistical Mechanics

10 pages, 6 figures

Scientific paper

10.1016/j.physa.2011.04.022

We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo process) with a variable jumping rate. Both the exponential and the algebraic form of the covariance -- defined for the truncated distribution -- are considered. It is demonstrated by numerical calculations that the stationary solution of the master equation for the case of power-law correlations decays with time, but a simple modification of the process makes the tails stable. The main result of the paper is a finding that -- in contrast to the velocity fluctuations -- the position variance may be finite. It rises with time faster than linearly: the diffusion is anomalously enhanced. On the other hand, a process which follows from a superposition of the Ornstein-Uhlenbeck-L\'evy processes always leads to position distributions with a divergent variance which means accelerated diffusion.

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